Through Hardships to the Stars: Tracking an Asteroid at YSPA

When I arrived at the Yale Summer Program in Astrophysics (YSPA), I expected to spend a lot of time learning about astronomy. What I did not expect was to spend four weeks repeatedly asking myself, “Where did our asteroid go?”

At YSPA, I worked on a research project with three other high school students from around the world. Together, we investigated a minor planet, specifically an asteroid, by collecting astronomical images, determining its position in the sky, predicting where it would appear next, and eventually calculating some of its physical and orbital properties.

Our project started with something that sounds pretty simple: a picture of the night sky.

Finding Our Asteroid

Astronomical surveys are essentially huge collections of images of the sky. By comparing images taken at different times, astronomers can identify objects that appear to move relative to the background stars. Most stars are so far away that they appear essentially stationary over the timescale of our observations, while objects within our Solar System, such as asteroids, can noticeably change position.

We looked through survey data and searched for these moving objects. Eventually, we selected one asteroid to follow throughout the four weeks of the program.

At first, our asteroid seemed like a great choice. It was relatively bright, so we expected it to be easy to detect in future observations. We thought that once we knew where it was, finding it again would be pretty straightforward.

We were very wrong.

We decided to nickname our asteroid “Aspera,” after YSPA’s motto, “Ad astra per aspera,” which means “through hardships to the stars.” The name seemed almost too appropriate. Aspera can be translated as “hardships,” and finding our asteroid repeatedly became one of the biggest challenges of our project.

Where Is Aspera?

To track Aspera, we needed to observe it repeatedly and determine its position in the sky.

We collected observations using the 0.4-meter and 0.25-meter telescopes at the Yale Leitner Observatory. We also used remotely operated telescopes in California through iTelescope, which allowed us to collect observations from a completely different location.

Our images contained much more than just the asteroid. Each image was filled with stars, galaxies, noise, and other objects. To analyze the images, we imported them into AstroImageJ, an astronomy-focused image-processing program.

Then came the tedious part: searching.

We would go through our images and compare the positions of objects from one image to another, looking for something that moved relative to the background stars. If we found a possible detection, we had to figure out whether it was actually Aspera or just another object, an image artifact, or noise.

And sometimes Aspera simply was not where we expected it to be.

This was one of the biggest lessons of the project. Knowing approximately where an asteroid should be does not mean that finding it is easy.

Turning a Dot of Light into Data

Once we identified Aspera in an image, we recorded its position using Right Ascension and Declination, usually shortened to RA and Dec.

If you have never encountered these coordinates before, they are basically the astronomical equivalent of latitude and longitude. Declination describes how far north or south an object is from the celestial equator, while Right Ascension describes its position around the celestial sphere.

By recording Aspera’s RA and Dec at different times, we could create a record of how the asteroid moved across the sky.

But simply knowing where Aspera had been was not enough. We needed to predict where it would be in the future.

Initially, we used a relatively simple linear regression model. We looked at how Aspera’s position changed over time and used that trend to estimate where it should appear next.

This worked reasonably well for short periods, but an asteroid’s motion is not actually a straight line across the sky. Its apparent motion depends on its orbit around the Sun, Earth’s own motion around the Sun, and the changing geometry between Earth, the asteroid, and the Sun.

So we needed a better model.

Building an Ephemeris

We eventually moved from our simple linear model to a more sophisticated ephemeris generator.

An ephemeris is essentially a prediction of where an astronomical object will be at a particular time. Instead of simply extending a straight-line trend, our model used observations of Aspera’s position at specific Julian Dates to predict its future position.

Julian Date is a continuous system for representing dates and times that is particularly useful in astronomy. Rather than having to deal with different calendar systems and complicated time conversions, astronomers can represent an observation with a single number.

Our program took the Right Ascension and Declination of Aspera at two specific Julian Dates and used numerical integration, specifically Verlet integration, to model its motion and predict its position at a new time.

This was where the project became much more than simply looking for an asteroid. We were using observations to build a mathematical model of an actual object in the Solar System.

Every new observation could also help us improve that model. The better our predictions became, the easier it was to know where to search for Aspera in our next set of images.

Eventually, we were able to calculate its orbital elements. Orbital elements are parameters that describe an object’s orbit, including its shape, orientation, and position along that orbit. Once these are known, they can be used to determine where the asteroid should be at different points in time.

After spending weeks chasing a tiny point of light across hundreds of images, being able to describe its orbit mathematically was incredibly satisfying.

Looking Beyond Where the Asteroid Is

Our project was not only about determining where Aspera was. We also wanted to learn more about the asteroid itself.

This is where photometry came in.

Photometry is the measurement of the brightness of astronomical objects. When we observe an asteroid through a telescope, the amount of light reaching the camera can be measured and converted into an instrumental magnitude.

Magnitude is a logarithmic system used by astronomers to describe brightness. However, our telescope and camera have their own characteristics, so the raw instrumental magnitude cannot be directly compared with measurements made by other telescopes.

To solve this, we used calibration stars with known magnitudes. By comparing the stars in our images with their catalogued values, we could calibrate our measurements and obtain a more meaningful magnitude for Aspera.

We also used observations through different filters to calculate its color index. A color index compares an object’s brightness in two different wavelength bands and gives us information about its color and, indirectly, some of its physical properties.

From these measurements, we could estimate properties such as the asteroid’s absolute magnitude, which is a standardized way of describing how bright an object would appear at a set distance.

So while tracking told us where Aspera was, photometry helped us learn more about what kind of object it was.

What We Learned About Aspera

By the end of the project, we determined that Aspera is a main-belt asteroid, meaning that it belongs to the large population of asteroids that orbit the Sun primarily between the orbits of Mars and Jupiter.

Our observations placed the asteroid at roughly 1.8 AU from Earth during our observations. One astronomical unit, or AU, is approximately the average distance between Earth and the Sun, so Aspera was about 1.8 times that distance from us at the time of our observations.

It is strange to think that the object we spent weeks searching for was just a tiny point of light in our images, yet that point represented an entire world orbiting the Sun.

Through Hardships to the Stars

The most memorable part of this project was not necessarily the final result. It was everything that happened in between.

There were nights when our observations did not go as planned. There were images where we could not confidently identify Aspera. There were predictions that needed to be revised, calculations that did not work the first time, and plenty of moments when we wondered whether we had lost our asteroid entirely.

But that was also what made the project feel like real astronomy.

Astronomy is not always about looking through a telescope and immediately seeing something spectacular. A lot of it is collecting imperfect data, figuring out what went wrong, developing better models, and trying again.

Our asteroid’s nickname ended up being more appropriate than we could have imagined. “Ad astra per aspera,” through hardships to the stars, was not just a motto printed on our program materials. It became a surprisingly accurate description of our research experience.

We started with a faint moving dot in a collection of survey images. Four weeks later, we had tracked that dot across the sky, built models to predict its motion, calculated its orbital elements, and used photometry to investigate its physical properties.

And somewhere out there, Aspera is still moving through the Solar System, completely unaware that four high school students spent an entire summer trying to find it.